Question

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.

Production Volume (units)	Total Cost ($)
400	3,700
450	4,700
550	5,100
600	5,600
700	6,100
750	6,700

a. Compute b₁ and b₀ (to 1 decimal).
b₁ [     ]
b₀ [     ]
Compute the estimated regression equation (to 1 decimal).
ŷ = [ ] + [ ]x

b. What is the variable cost per unit produced (to 1 decimal)?
$[     ]

c. Compute the coefficient of determination (to 3 decimals). Note: report r² between 0 and 1.
r² = [     ]
What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)?
[     ]%

d. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to the nearest whole number)?
$[     ]

Answer 1

using excel data analysis tool for regression, following o/p is obtained

Regression Statistics
Multiple R	0.9791
R Square	0.9587
Adjusted R Square	0.9484
Standard Error	241.523
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5415000.000	5415000	92.83	0.0006
Residual	4	233333.333	58333
Total	5	5648333.333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	946.667	464.160	2.04	0.1110	-342.048	2235
X	7.600	0.789	9.635	0.0003	5.410	9.790

a)

bo = 946.7

b1 = 7.6

Ŷ =   946.7 +   7.6 *x

b)

variable cost per unit produced $7.6

c)

the coefficient of determination ,r²=0.9587

95.9% percentage of the variation in total cost can be explained by the production volume

d)

Ŷ =   946.67   +   7.60   *x

X=500

Ŷ =   946.67   +   7.60   *500 = 4746.667

so, estimated total cost for this operation is $4747